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Example 6--Page 2We want . Looking at the right side we want to get from the left side. We know by the Product to Sum formulas, sine multiplied by cosine will become sine plus sine, and , , ; , , . So we will get and , but by using the Derived formula, . We reach our goal. Since . Now for the second factor, we still didn't reach the goal , and cancel . But we see it is simpler than the last step. Same idea, we want . It looks like the Sum to Product formulas. If we use the Sum to Product formula of sines immediately, we have . The right side of it is not . We need , not ! How can we get ? If we use the Derived formulas we have , which is what we want. The identity has been proven. This problem is a little bit more difficult than the previous ones. You can see that Derived formulas are very useful for actual angle identities. |
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